x = 3k (where k is a positive integer)
y = 4z (where z is a positive integer)
xy = 12kz = 3*2*2 kz

Now let us take a look at the options

I. 6

xy already contains a 3 and a 2 so IT MUST BE A MULTIPLE OF 6

II. 9

xy contains one 3 so if k/z contains a 3, then it can be a multiple of 9, else not. So, not certain

III. 12

xy already contains a 3 and two 2's so IT MUST BE A MULTIPLE OF 12

Answer - D